Skip to main content Accessibility help
×
Home

An ellipsoidal particle in tube Poiseuille flow

  • Haibo Huang (a1) and Xi-Yun Lu (a1)

Abstract

A suspended ellipsoidal particle inside a Poiseuille flow with Reynolds number up to 360 is studied numerically. The effects of tube diameter ( $D$ ), inertia of the particle and the flow, and the particle geometry (both prolate and oblate ellipsoids) are considered. When a prolate particle with $a/b=2$ is inside a wider tube (e.g.  $D/A>1.9$ ), where $A=2a$ is the length of the major axis of the particle, the terminal stable state is tumbling. When the prolate particle is inside a narrower tube ( $1.0<D/A<1.9$ ), log-rolling or kayaking modes may appear. Which mode occurs depends on the competition between fluid and particle inertia. When the fluid inertia is dominant, the log-rolling mode appears, otherwise, the kayaking mode appears. Inclined and spiral modes may appear when $D/A<1$ and $D/A=1$ , respectively. For a prolate ellipsoid with $a/b=4$ , if $1<D/A<1.9$ , there is only the kayaking mode and the log-rolling mode is not observed. When an oblate particle is inside a wider tube (e.g.  $D/A>3.5$ ), it may adopt the log-rolling mode. Inclined and intermediate modes are firstly identified in narrower tubes. The phase diagram of the modes is also provided. The modes in the phase diagrams were not found to be affected by the initial state of the particle based on limited observation.

Copyright

Corresponding author

Email address for correspondence: huanghb@ustc.edu.cn

References

Hide All
Aidun, C. K., Lu, Y. & Ding, E.-J. 1998 Direct analysis of particulate suspensions with inertia using the discrete Boltzmann equation. J. Fluid Mech. 373, 287311.
Byeon, H. J., Seo, K. W. & Lee, S. J. 2015 Precise measurement of three-dimensional positions of transparent ellipsoidal particles using digital holographic microscopy. Appl. Opt. 54 (8), 21062112.
Chen, Y., Cai, Q.-D., Xia, Z.-H., Wang, M.-R. & Chen, S.-Y. 2013 Momentum-exchange method in lattice Boltzmann simulations of particle–fluid interactions. Phys. Rev. E 88 (1), 013303.
D’Avino, G., Greco, F. & Maffettone, P. L. 2015 Rheology of a dilute viscoelastic suspension of spheroids in unconfined shear flow. Rheol. Acta 54 (11–12), 915928.
D’Avino, G. & Maffettone, P. L. 2015 Particle dynamics in viscoelastic liquids. J. Non-Newtonian Fluid Mech. 215, 80104.
Ding, E. & Aidun, C. K. 2000 The dynamics and scaling law for particles suspended in shear flow with inertia. J. Fluid Mech. 423, 317344.
Einarsson, J., Candelier, F., Lundell, F., Angilella, J. R. & Mehlig, B. 2015 Rotation of a spheroid in a simple shear at small Reynolds number. Phys. Fluids 27 (6), 063301.
Feng, J., Hu, H. H. & Joseph, D. D. 1994 Direct simulation of initial value problems for the motion of solid bodies in a Newtonian fluid. Part 2. Couette and Poiseuille flows. J. Fluid Mech. 261, 95134.
Huang, H., Wu, Y. & Lu, X.-Y. 2012a Shear viscosity of dilute suspensions of ellipsoidal particles with a lattice Boltzmann method. Phys. Rev. E 86 (4), 046305.
Huang, H., Yang, X., Krafczyk, M. & Lu, X.-Y. 2012b Rotation of spheroidal particles in Couette flows. J. Fluid Mech. 692, 369394.
Huang, H., Yang, X. & Lu, X.-Y. 2014 Sedimentation of an ellipsoidal particle in narrow tubes. Phys. Fluids 26 (5), 053302.
d’Humiéres, D., Ginzburg, I., Krafczyk, M., Lallemand, P. & Luo, L.-S. 2002 Multiple-relaxation-time lattice Boltzmann models in three dimensions. Phil. Trans. R. Soc. Lond. A 360, 437451.
Jeffery, G. B. 1922 The motion of ellipsoidal particles immersed in a viscous fluid. Proc. R. Soc. Lond. A 102 (715), 161179.
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1963 Axial migration of particles in Poiseuille flow. Nature 200, 159160.
Karnis, A., Goldsmith, H. L. & Mason, S. G. 1966 The flow of suspensions through tubes: V. inertial effects. Can. J. Chem. Engng 44 (4), 181193.
Ladd, A. J. C. 1994a Numerical simulations of particulate suspensions via a discretized Boltzmann equation. Part 1. Theoretical foundation. J. Fluid Mech. 271, 285309.
Lallemand, P. & Luo, L.-S. 2003 Lattice Boltzmann method for moving boundaries. J. Comput. Phys. 184 (2), 406421.
Mei, R. W., Luo, L.-S. & Shyy, W. 1999 An accurate curved boundary treatment in the lattice Boltzmann method. J. Comput. Phys. 155 (2), 307330.
Pan, T.-W., Chang, C.-C. & Glowinski, R. 2008 On the motion of a neutrally buoyant ellipsoid in a three-dimensional Poiseuille flow. Comput. Meth. Appl. Mech. Engng 197 (25), 21982209.
Qi, D.-W. 1999 Lattice-Boltzmann simulations of particles in non-zero-Reynolds-number flows. J. Fluid Mech. 385, 4162.
Qi, D.-W. & Luo, L.-S. 2003 Rotational and orientational behaviour of three-dimensional spheroidal particles in Couette flows. J. Fluid Mech. 477, 201213.
Qi, D.-W., Luo, L.-S., Aravamuthan, R. & Strieder, W. 2002 Lateral migration and orientation of elliptical particles in Poiseuille flows. J. Stat. Phys. 107 (1–2), 101120.
Rosén, T., Einarsson, J., Nordmark, A., Aidun, C. K., Lundell, F. & Mehlig, B. 2015 Numerical analysis of the angular motion of a neutrally buoyant spheroid in shear flow at small Reynolds numbers. Phys. Rev. E 92 (6), 063022.
Rosén, T., Lundell, F. & Aidun, C. K. 2014 Effect of fluid inertia on the dynamics and scaling of neutrally buoyant particles in shear flow. J. Fluid Mech. 738, 563590.
Rosén, T., Nordmark, A., Aidun, C. K., Do-Quang, M. & Lundell, F. 2016 Quantitative analysis of the angular dynamics of a single spheroid in simple shear flow at moderate Reynolds numbers. Phys. Rev. Fluids 1 (4), 044201.
Segre, G. & Silberberg, A. 1961 Radial particle displacements in Poiseuille flow of suspensions. Nature 189, 209210.
Sugihara-Seki, M. 1996 The motion of an ellipsoid in tube flow at low Reynolds numbers. J. Fluid Mech. 324, 287308.
Swaminathan, T. N., Mukundakrishnan, K. & Hu, H. H. 2006 Sedimentation of an ellipsoid inside an infinitely long tube at low and intermediate Reynolds numbers. J. Fluid Mech. 551, 357385.
Villone, M. M., D’Avino, G., Hulsen, M. A. & Maffettone, P. L. 2015 Dynamics of prolate spheroidal elastic particles in confined shear flow. Phys. Rev. E 92 (6), 062303.
Xia, Z., Connington, K. W., Rapaka, S., Yue, P., Feng, J. J. & Chen, S.-Y. 2009 Flow patterns in the sedimentation of an elliptical particle. J. Fluid Mech. 625, 249272.
Yang, B. H., Wang, J., Joseph, D. D., Hu, H. H., Pan, T.-W. & Glowinski, R. 2005 Migration of a sphere in tube flow. J. Fluid Mech. 540, 109131.
Yang, X., Huang, H. & Lu, X.-Y. 2015 Sedimentation of an oblate ellipsoid in narrow tubes. Phys. Rev. E 92 (6), 063009.
Yu, Z. S., Phan-Thien, N. & Tanner, R. I. 2004 Dynamic simulation of sphere motion in a vertical tube. J. Fluid Mech. 518, 6193.
Yu, Z.-S., Phan-Thien, N. & Tanner, R. I. 2007 Rotation of a spheroid in a Couette flow at moderate Reynolds numbers. Phys. Rev. E 76 (2), 026310.
Zhu, M.-Y.2000 Direct numerical simulation of solid-liquid flow of Newtonian and viscoelastic fluids. PhD thesis, University of Pennsylvania.
MathJax
MathJax is a JavaScript display engine for mathematics. For more information see http://www.mathjax.org.

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed